: : : In the usage I'm familiar with (U.S.), it simply means to talk long and tirelessly. ~rb

: : It looks like you're right rb. I should have gone to US dictionaries to confirm my understanding. I'm guilty of inferring a meaning from the context in which I most often find the phrase; and, possibly, of confusing the phrase with "swear a blue streak". In my defence I could say that this context is quite common, as witness the example attached.

: Oh dear. The link didn't come out; perhaps because I didn't give it a title. Let's try again

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"Streak" usually implies speed, as in "streak of lightning," or "the nude students streaked through the classroom" (which gave rise to the use of the verb "streak" to describe this particular activity without further explanation needed). "Blue" is often added for emphasis or rhythm. I don't think that "blue" implying raciness or vulgarity is the "blue" at work in "blue streak." Cf. the OED:

1830 Kentuckian 14 May, To pass..with such rapidity as not even to leave a '*blue streak' behind him. 1847 Knickerbocker XXX. 178 Interspersing his vehement comments with a 'blue streak' of oaths. 1895 S. HALE Lett. 289, I..drove in her sort of..carryall..talking a blue streak two miles to her house. 1937 RUNYON More than Somewhat iii. 64 She hears..a guy cussing a blue streak. 1949 Landfall III. 236 Sid was talking a blue streak to Jean. 1968 'R. RAINE' Night of Hawk xxii. 109, I was talking a blue streak, my expression like thunder."

I don't wish to suggest that "streak" ALWAYS implies speed. Used as a noun, streak most often refers to a line, mark, stroke, or band of color (as in a streak of blond in an otherwise colored head of hair).
SS